A119030 Difference between numerator and denominator of the sum of all matrix elements of n X n Hilbert matrix M(i,j)=1/(i+j-1) (i,j = 1..n), A117731[n] - A117664[n].

0, 4, 27, 428, 1375, 15797, 211631, 86540, 1496205, 144045379, 145607407, 3378951221, 17021747431, 51392118293, 214084856611, 13337033800292, 13393340889767, 94103945740529, 3493457389196573, 3503912518228613

Offset: 1

Author

Alexander Adamchuk, Jul 22 2006

Keywords

• nonn

Comments

p^3 divides a(p^k) for prime p>2 and integer k>0.

Crossrefs

Cf. A117731, A117664.

Programs

Mathematica

Numerator[Table[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}],{n,1,25}]] - Denominator[Table[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}],{n,1,25}]]

Formula

a(n) = Numerator[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}]] - Denominator[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}]]. a(n) = A117731[n] - A117664[n].